Does the distributive property contradict the rules of order of
operations? When we have a(b + c) order of operations says we should
add first in the parentheses, then multiply, but the distributive
property says we can multiply first to get ab + ac, then add.

I get confused about which number goes where when I have to do something like "6 divided by 2". Which number goes in the calculator first? And which number goes on the outside and inside if I am doing it on paper?

How can I convince a 14 year old girl who is in 8th grade the
importance of mental math? I think that skills like mentally adding
and subtracting 2 digit numbers and being able to estimate multiplying
2 digit large numbers are critical. My daughter's teacher says that
such skills aren't needed because of calculators and computers.